This work presents a mathematical model to evaluate heat losses of a sensible heat storage tank for a concentrated solar power plant with solar salt as the storage material. The transient mathematical model takes into account the heat losses to the environment by evaluating the levels of solar irradiation, ambient temperature, and wind speed. Besides that, the model is simple and flexible and may not require considerable computational power. The model was validated using published experimental data for the solar power plants Solar Two and Andasol I. The transient analysis was performed by solving the diffusive terms of the differential equations resulting from energy balance and heat exchanges using the Finite Difference Method (FDM) in the implicit formulation for system discretization and the TriDiagonal Matrix Algorithm (TDMA) for solving the equations. This model allows evaluating individually the effects of several parameters inherent to the thermal storage system by two tanks. In this paper, thermal losses and storage efficiency were evaluated regarding the effects of climatic conditions, loading level, and operating temperature. Heat loss rates calculated by the proposed model differ from the experimental results by 4.55% for the hot tank, and 4.82% for the cold tank. The tank had no significant sensitivity to climatic conditions exhibiting a difference of less than 1% for storage efficiency. Heat losses relatively sensitive to the tank loading level, presenting a difference of 37.35% between the loaded and unloaded tank. The operating temperatures were also quite influential on the thermal storage efficiency, being 10.78% for the tank at 300 degrees C and 89.42% for the tank at 600 degrees C. In general, the tank showed little sensitivity to changes in climatic conditions, however, it showed considerable sensitivity to loading level and operating temperature. The heat loss of a heat storage system is a function of many variables and understanding the influence of each parameter in the system is essential for technological advances.